To graph the line represented by the equation $y = -x - 6$, follow these steps:

1. Identify the Slope and Y-intercept:

   • The equation is in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
   • Here, $m = -1$ and $b = -6$. So, the slope is $-1$ and the y-intercept is $-6$.

2. Plot the Y-intercept:

   • Start by plotting the point $(0, -6)$ on the graph. This is where the line crosses the y-axis.

3. Use the Slope to Find Another Point:

   • The slope $-1$ means that for every 1 unit you move to the right on the x-axis, you move 1 unit down on the y-axis.
   • From the point $(0, -6)$, move 1 unit right (to $x = 1$) and 1 unit down (to $y = -7$), giving you the point $(1, -7)$.

4. Draw the Line:

   • Using the points $(0, -6)$ and $(1, -7)$, draw a straight line through them. This line extends across the graph in both directions.

This will create the graph for the line $y = -x - 6$.

Would you like further details on graphing lines, or do you have any questions?

Related Questions:

1. How do you determine the slope and y-intercept from an equation?
2. What steps would change if the slope were positive?
3. How can you graph a line using the x-intercept and y-intercept?
4. What happens to the line if you change the equation to $y = -2x - 6$?
5. How do you convert between different forms of linear equations?

Tip: When the slope is negative, the line falls from left to right.